Question

Решите пожалуйста
x^(log 0,5 x -1) = 1/64

Answer 1

x^(log(0,5)(х-1))=1/64
x>0

log(2)x^(log(05)(x-1)=log(2)1/64
log(0,5)(x-1)*log(2)x=-6
(-log(2)x-1)log(2)x=-6
log(2)x=t
(-t-1)*t=-6

t²+t-6=0
D=1+24=25=5²
t=(-1±5)/2
t1=-3
t2=2
log(2)x=-3;x=1/8
log(2)x=2;x=4
ответ 4;1/8